Abstract

Characterizing nanoparticles in terms of size and morphology is essential to understand their physical and optical properties. Small-Angle X-ray Scattering (SAXS) is a powerful in situ technique that allows the analysis of such nanostructures exhibiting size and morphology through the Guinier and Porod regimes, which can be repeated at different scales (e.g., primary spheres and aggregates for mass fractal aggregates, as focused on in this study). This is the principle of the widely used Beaucage unified model, built in reciprocal q-space. However, by definition, the scattered signal corresponds to the Fourier transform of the particles’ pair correlation, enabling alternative modeling based on the pair correlation itself. The present study examines whether the Beaucage model aligns with recent pair correlation models for point-touching sphere fractal aggregates. Both approaches are applied to SAXS data from soot particles in a laminar ethylene diffusion flame measured at the European Synchrotron Radiation Facility (ESRF) and processed via Abel inversion. The models are compared in terms of data fitting and their impact on parameters including primary particle size distribution, invariant parameter, and specific surface area. The results highlight the need for further investigations of the modelling of pair correlation function for fractal aggregates. © 2025, Begell House Inc. All rights reserved.